Answer to Question #13813 in Calculus for Alyssa Jennings

Question

I need steps to follow as well, please.
f(x) = x-4
g(x)= 3x^2
find (fog)(x) and (gof)(x)
Detailed expanation

Answer 1

We're dealing with function composition which is the application of one function to the results of another. It's defined as
(g ∘ f)(x) = g(f(x))

So (fog)(x)=f(g(x))=g(x)-2=3x^2-4
Here to find the required composition we place expression for g instead of x in the expression for f.

Similarly (gof)(x)=g(f(x))=3f(x)^2=3(x-4)^2